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Understanding the morphology of growing crystals under different conditions is a fundamental problem that has implications in a wide variety of systems like electronic and optoelec-tronic devices and biological systems like kidney stone growth and abalone shell growth. Over the years our group has been using techniques from nonequilibrium statistical mechanics and computer simulation to address different aspects of this problem. One major area where we are actively working in is heteroepitaxy, wherein a crystalline film is grown on a crystalline substrate of a different material. The difference in the two materials leads to a strain in the growing film that can lead to a change in the nature of the growing surface. A very well-studied example of such a system is the Germanium on Silicon(001) surface. Experiments have revealed that the growth of the Ge film is flat for the first three atomic layers but becomes mounded for layers after that. The size and shapes of the mounds have been characterized experimentally and several theoretical approaches have been proposed to explain the growth features. To address this problem, we adopt the technique of lattice-based kinetic Monte Carlo simulatations with explicit elastic effects. Through our calculations we have investigated the interplay between the inherent anisotropy in the surface energy of the Ge film and the strain effects due to the mismatch with the substrate. In addition to the Silicon-Germanium system, we are also looking at Galium Nitride based systems using similar lattice-based kinetic Monte Carlo simulations. In this case, there are additional complexities due to the multiple species involved in the growth process. Further, we have also worked on crystal growth from impure solutions wherein impurities can completely stop growth, even when the solution is supersaturated in the growing species. We model the process of crystal growth via the motion of surface steps and show how impurities can cause step-bunching, step-pinning and the coherent motion of step bunches. Another area where we are actively working is in problems in bioinformaics and biophysical chemistry. Our work included statistical analysis of Genetic expression information at multiple time-stages and the analysis of transport of Calcium across the neuronal cells.